The aim of this study is to test the effect of the combination of valproate in combination with imatinib with an aim of achieving a maximal molecular response as the primary goal. Briefly, patients with CML who are taking imatinib and have been found to have a plateau in their level of the bcr-abl transcript will be eligible to participate in the study. Valproate will then be added to the imatinib, and subsequent bcr-abl transcripts will be monitored to see if the addition of valproate produced a further reduction. Patients will be monitored for efficacy and toxicity.